Performance of an adaptive LQ controller with periodic exitation

We present a tutorial example to demonstrate the applicability of the techniques of the theory of stochastic complexity to compute the effect of parameter uncertainty onto control performance. A simple continuous-time linear quadratic adaptive controller with injected sinusoid signal will be considered. The effect of the intensity of the injected signal on the cost function will be determined. The result has close connections with earlier works on the interaction of identification and control presented in [3, 2, 14, 15].